Whenever voltages (or any parameters represented by voltages) need to be measured or digitized, it is necessary to have a voltage reference. Most electronic devices of any complexity have one or more references, for example in a signal processing chain or in the power supply circuitry.
Depending on the desired overall system accuracy, the requirements for voltage references vary greatly; however it is clear that if well designed, a voltage reference should be relatively insensitive to deviations in its own power supply and to variations in its temperature.
As with any other engineering challenge, the design of a voltage reference forces tradeoffs. Designing a voltage reference to be highly accurate despite changes in temperature, for example, usually makes it much more expensive.
The designer of a voltage reference, in pursuit of temperature stability, will usually draw upon a bit of good luck, which is that nature will sometimes be so cooperative as to make it possible to develop a first circuit yielding a voltage having a linear relationship to temperature (with some first measurable coefficient) over some useful dynamic range, and to develop a second circuit yielding a voltage having a linear relationship to temperature (with some second measurable coefficient non-identical to the first coefficient) over that same useful dynamic range. It is particularly helpful if the two coefficients differ in sign; this prompts designers to utilize the scheme illustrated in FIG. 1. This figure shows two voltages (Vn and Vp), each having a prescribed relationship to the changes in temperature. Nature cooperates by providing one voltage that is decreasing when the temperature is increasing, commonly called CTAT or Complimentary To Absolute Temperature; and by providing another voltage that is increasing when the temperature is increasing, commonly called PTAT or Proportional To Absolute Temperature.
With these two voltages available, the designer applies an appropriate linear amplification to one of the voltages in order to make the rates of change, created by temperature changes, of both voltages equal in magnitude but with opposite signs. Then, the two voltages are added together, with a resulting sum that is relatively temperature independent.
In the example of FIG. 1, we see that the slope of the PTAT line is shallower, so the voltage that gets amplified is the PTAT voltage. The gain of the amplification is selected so that the slope of the K*Vp line is (as closely as is possible) equal and opposite to that of the Vn line. The goal of course is that the sum of these two will be relatively temperature independent.
One common method for the establishment of the CTAT and PTAT voltages is the utilization of semiconductor diodes (or bipolar transistors), which are behaving according to the “classic” Shockley diode equation shown in FIG. 4(a). An approximate relationship may be derived from the Shockley diode equation:V1−V2=ΔVd=(nk/q)*T*In(J1/J2)  [Equation 1]where:                V1 and V2 are the voltages formed by forward-biasing the diodes with currents that establish current densities J1 and J2;        quantity (nk/q) is (for the present purposes) a constant; and        T is the absolute (Kelvin) temperature.        
From Equation 1 we see that the difference voltage ΔVd has a PTAT characteristic.
At the same time, the forward voltage of the diode has CTAT characteristics due to temperature dependency of the quantity Is in the Shockley diode equation (FIG. 4(a)).
Most of the present-day low-voltage (below five volts) voltage references are based on the above principles. Prior art circuits depicting the groundbreaking actual realizations are shown in FIG. 2 (Widlar) and FIG. 3 (Brokaw).
From FIGS. 2 and 3 we see that each of these circuits utilitizes and indeed depends for its accuracy upon matched semiconductor devices.
The circuit in FIG. 2, for example, develops its diode voltage difference due to differing currents passing through equal and matched units.
The circuit in FIG. 3 develops the diode voltage difference due to specifically designed sizes of the matched units, so that approximately the same current will create differing current densities which are inversely proportional to the size of the respective junction. Notice the notation “8A” that signifies that the device in location Q2 is to be eight times larger than the device in location Q1. One way to do this, of course, is to create this larger device at Q2 by simply connecting eight devices equivalent to Q1 in parallel.
The alert reader will thus appreciate that the degree of success in making the voltage reference circuit accurate despite changes of temperature depends greatly upon the degree of success in either the matching of similar devices (FIG. 2), or the degree of success in bringing about some particular physical ratio of size (FIG. 3).
In order to provide sufficiently-matched components, the designers have to resort to making the matched devices very large, so that the geometrical processing errors in the manufacture of the integrated circuits (ICs) have a diminishing effect on the matching; however, this increases the costs of manufacture, as more area is required on the surface of the IC die. This also uses up die real estate that could have been given to some other purpose.
The alert reader will also have appreciated that the accuracy of Equation 1 depends on both semiconductor devices having exactly the same temperature. Saying the same thing differently, if the two devices were to be at non-identical temperatures, then the results of Equation 1 would be less helpful in providing a temperature compensation mechanism for a voltage reference.
The approaches of FIG. 2 or 3 thus lead to a further design goal which is to reduce to a minimum the temperature difference between the two junctions. One design approach toward this goal includes splitting each of the matched devices into several parallel-connected units, and positioning the units utilizing geometrical symmetry considerations. But the fact remains that a temperature gradient inside the IC will create errors, and these errors cannot be completely eradicated.
Helpful background information may be found at:                W. B. Shockley, “Electrons and Holes in Semiconductors,” Van Nostrand, 1950.        R. J. Widlar, “New Developments in IC Voltage Regulators,” IEEE Journal of Solid-State Circuits, vol. SC-6, no. 1, pp. 2-7, February 1971.        A. P. Brokaw, “A Simple Three-Terminal IC Bandgap Reference,” IEEE Journal of Solid-State Circuits, vol. SC-9, no. 6, pp. 388-393, December 1974.        Y. P. Tsividis, “Accurate Analysis of Temperature Effects in Ic-Vbe Characteristics with Application to Bandgap Reference Sources,” IEEE Journal of Solid-State Circuits, vol. SC-15, no. 6, pp. 1076-1084, December 1980.        U.S. Pat. No. 4,384,217 to Tsividis.        
From the above discussion it may be seen that it would be very helpful if some approach could be found by which a voltage reference could be temperature compensated without the many drawbacks discussed.